Analysis of Two-Grid Characteristic Finite Element Methods for Convection-Diffusion Equations. (18th January 2023) - Wang, Keyan; Hu, Boxia
Abstract : In this paper, two efficient two-grid algorithms for the convection-diffusion problem with a modified characteristic finite element method are studied. We present an optimal error estimate in L p -norm for the characteristic finite element method unconditionally, while all previous works require certain time-step restrictions. To linearize the characteristic method equations, two-grid algorithms based on the Newton iteration approach and the correction method are applied. The error estimate and the convergence result of the two-grid method are derived in detail. It is shown that the coarse space can be extremely coarse and achieve asymptotically optimal approximations as long as the mesh sizes H = O h 1 / 3 in the first algorithm and H = O h 1 / 4 in the second algorithm, respectively. Finally, two numerical examples are presented to demonstrate the theoretical analysis.